Quantization of derived cotangent stacks and gauge theory on directed graphs

Marco Benini, Jonathan P. Pridham, Alexander Schenkel
January 25, 2022
We study the quantization of the canonical unshifted Poisson structure on the derived cotangent stack $T^\ast[X/G]$ of a quotient stack, where $X$ is a smooth affine scheme with an action of a (reductive) smooth affine group scheme $G$. This is achieved through an \'etale resolution of $T^\ast[X/G]$ by stacky CDGAs that allows for an explicit description of the canonical Poisson structure on $T^\ast[X/G]$ and of the dg-category of modules quantizing it. These techniques are applied to construct a dg-category-valued prefactorization algebra that quantizes a gauge theory on directed graphs.

Derived algebraic geometry, derived cotangent stack, quotient stack, Deformation quantization, lattice gauge theory